Consumer Choice Using Utility Theory In February 2006, Apple Computer sold its billionth song at its iTunes music store. Economics: Principles and Tools O’Sullivan, Sheffrin, Perez 6/e. P R E P A R E D B Y FERNANDO QUIJANO, YVONN QUIJANO, AND XIAO XUAN XU

A P P L Y I N G T H E C O N C E P T S How does a tax on one good affect the demand for substitute goods? New Zealand’s Tax on Light Spirits Why do consumers dislike the bundling of goods? Online Music Stores and Piracy How do consumers respond to offsetting changes in taxes? The Substitution Effect of a Gas Tax Decreases Gas Consumption How do consumers respond to free goods? The Big Difference between $0.20 and FREE! How does product branding affect consumers’ brain activity? Neuroscience and the Cola Challenge 1 2 3 4 5

7.1 TOTAL AND MARGINAL UTILITY utility The satisfaction experienced from consuming a good. util One unit of utility.

7.1 TOTAL AND MARGINAL UTILITY ► FIGURE 7.1 Total Utility and Marginal Utility In Panel A, the total utility or satisfaction from downloaded songs increases with the number of songs, but at a decreasing rate. In Panel B, the marginal utility from songs decreases as the number of songs increases.

7.1 TOTAL AND MARGINAL UTILITY marginal utility The change in total utility from one additional unit of a good. law of diminishing marginal utility As the consumption of a particular good increases, marginal utility decreases.

7.2 Consumer Constraints: The Budget Line CONSUMER CHOICE budget line The line connecting the combinations of two goods that exhaust a consumer’s budget. budget set The set of affordable combinations of two goods.

7.2 Consumer Constraints: The Budget Line CONSUMER CHOICE  FIGURE 7.2 Budget Set and Budget Line The budget set (the shaded triangle) shows all the affordable combinations of books and movies, and the budget line (with endpoints a and k) shows the combinations that exhaust the budget.

7.2 Making Choices Using the Equimarginal Rule CONSUMER CHOICE Pick the combination of two activities where the marginal benefit per dollar for the first activity equals the marginal benefit per dollar for the second activity.

7.2 Making Choices Using the Equimarginal Rule CONSUMER CHOICE Pick the combination of two activities where the marginal benefit per dollar for the first activity equals the marginal benefit per dollar for the second activity.

A P P L I C A T I O N 1 NEW ZEALAND’S TAX ON LIGHT SPIRITS APPLYING THE CONCEPTS #1: How does a tax on one good affect the demand for substitute goods? How did teenagers in New Zealand respond to a special tax on their favorite alcoholic beverage? We can use the equimarginal rule to explore New Zealand’s recent experiences with taxing alcoholic beverages. “Light spirits”—beverages with alcohol content between 14 and 24 percent—provided the biggest alcoholic bang per buck for teens. The government imposed a special tax on light spirits, nearly doubling the price. The tax decreased the bang per buck and teens responded by cutting back. Producers responded by changing their beverage recipes to avoid the tax. Moreover, they priced these new “super-light” beverages below the original light beverage price. Given the equimarginal rule, we would expect many teens to switch to super-light beverages, and that’s exactly what happened. The simple lesson is that consumers respond to taxes and changes in price.

A P P L I C A T I O N 2 ONLINE MUSIC STORES AND PIRACY APPLYING THE CONCEPTS #2: Why do consumers dislike the bundling of goods? Online music stores provide an alternative to buying bundles of songs on CDs. We can use the theory of consumer choice to explain the logic behind this recent development.  FIGURE 7.3 Internet Music Piracy and iTunes When music is sold as 15-song bundles on CDs, the consumer has three budget points (a, c, and d) rather than an entire budget line. If songs are sold individually, the consumer has a complete budget line and can legally reach his or her ideal combination of 6 songs and 48 arcade games (point b).

7.3 THE INDIVIDUAL DEMAND CURVE An individual demand curve shows the relationship between the price of a product and the quantity demanded by a rational consumer. In other words, the demand curve shows, for each price, the utility-maximizing quantity for the consumer.  FIGURE 7.4 The Individual Demand Curve When the price of a movie is $3, Maxine maximizes utility at point i, with four movies. If the price drops to $2, she maximizes utility at point j, with seven movies.

7.3 The Income and Substitution Effects of a Price Change THE INDIVIDUAL DEMAND CURVE 7.3 The Income and Substitution Effects of a Price Change substitution effect The change in quantity consumed that is caused by a change in the relative price of the good, with real income held constant. income effect The change in quantity consumed that is caused by a change in real income, with relative prices held constant.

7.3 The Income and Substitution Effects of a Price Change THE INDIVIDUAL DEMAND CURVE 7.3 The Income and Substitution Effects of a Price Change Points on the Demand Curve In general, each point on a demand curve shows the utility-maximizing choice for a particular price.

A P P L I C A T I O N 3 THE SUBSTITUTION EFFECT OF A GAS TAX DECREASES GAS CONSUMPTION APPLYING THE CONCEPTS #3: How do consumers respond to offsetting changes in taxes? If the government raises the gasoline tax and cuts income taxes, will gasoline consumption decrease? Initial price of gas = $4 per gallon Price of another good = $1 per unit When the consumer maximizes utility, gas consumption is 1,000 gallons per year and the marginal utility of gas = 12 utils. The marginal utility of the other good = 3 utils. This yields the equimarginal principle: Then, a tax of $2 is imposed on gasoline. The price of gas after tax = $4 + $2 = $6, and the equimarginal principle is affected as follows: The citizen will cut back on gasoline and spend more on the other good. The decrease in gas consumption is the substitution effect in action.

7.4 CONSUMER PUZZLES—FREE GOODS AND BRANDING A P P L I C A T I O N 4 THE BIG DIFFERENCE BETWEEN $0.20 AND FREE! APPLYING THE CONCEPTS #4: How do consumers respond to free goods? A few years ago Amazon.com introduced free shipping for U.S. orders over $25. A consumer who bought a single book for less than $25 would pay about $4 in shipping, but if adding a second book to the order brought the book total to at least $25, shipping was free. The free-shipping offer decreased the effective price of any book that pushed the book order over $25, and sales increased dramatically. In France, the company offered cheap—but not free—shipping for orders over $25. Crossing the $25 threshold cut the shipping charge to only 1 franc, about $0.20. In contrast with the U.S. experience, book sales increased by a relatively small amount. The Amazon experiences in the United States and France illustrate a puzzle in consumer behavior. Cutting the shipping charge from $4 to zero had a huge effect, but cutting the charge to $0.20 didn’t have much of an effect. Consumers are highly responsive to freebies, and many firms incorporate free goods and services into their marketing.

A P P L I C A T I O N 5 NEUROSCIENCE AND THE COLA CHALLENGE APPLYING THE CONCEPTS #5: How does product branding affect consumers’ brain activity? In the “Pepsi Challenge” advertisements, randomly chosen consumers tasted Pepsi and Coke, and a majority preferred Pepsi. In an advertising campaign running at the same time, Coca-Cola proclaimed that a majority of consumers who tasted both products actually preferred Coke. Can both companies be correct? There was a subtle difference between the two taste tests. Pepsi used blind tasting, while Coca-Cola used nonblind tasting. When consumers don’t know what brand they are drinking, Pepsi has the edge. In other words, branding makes a difference. Neuroscientists ran the cola challenge while monitoring the brain activity of the tasters. When the participants knew which brand they were drinking, the portion of the brain involved in higher order functions—working memory, associations, higher-order cognitions, and ideas—was stimulated, and the activation was much greater with Coke than with Pepsi. In other words, branding affects brain activity and consumer preference.

K E Y T E R M S budget line budget set equimarginal rule income effect law of diminishing marginal utility marginal utility substitution effect util utility

CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 7 A P P L Y I N G T H E C O N C E P T S To determine whether a consumer is making the best choice, what single question can you ask? What’s Your MRS? Why do consumers dislike the bundling of goods? Online Music and Piracy How do consumers respond to free goods? The Big Difference between $0.20 and FREE! How do consumers respond to offsetting changes in taxes? The Substitution Effect of a Gas Tax Decreases Gas Consumption 1 2 3 4

7A.1 Consumer Constraints: The Budget Set and Budget Line CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 7 7A.1 CONSUMER CONSTRAINTS AND PREFERENCES Consumer Constraints: The Budget Set and Budget Line budget line The line connecting all the combinations of two goods that exhaust a consumer’s budget. budget set A set of points that includes all the combinations of two goods that a consumer can afford, given the consumer’s income and the prices of the goods. price ratio The price of the good on the horizontal axis divided by the price of the good on the vertical axis.

7A.1 Consumer Constraints: The Budget Set and Budget Line CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 7 7A.1 CONSUMER CONSTRAINTS AND PREFERENCES Consumer Constraints: The Budget Set and Budget Line FIGURE 7A.1 Budget Set and Budget Line The budget set (the shaded triangle) shows all the affordable combinations of books and movies, and the budget line (with endpoints a and k) shows the combinations that exhaust the budget.

7A.1 Consumer Preferences: Indifference Curves CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 7 7A.1 CONSUMER CONSTRAINTS AND PREFERENCES Consumer Preferences: Indifference Curves utility The satisfaction experienced from consuming a good. indifference curve A curve showing the different combinations of two goods that generate the same level of utility or satisfaction. marginal rate of substitution (MRS) The rate at which a consumer is willing to trade or substitute one good for another.

7A.1 CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 7 7A.1 CONSUMER CONSTRAINTS AND PREFERENCES FIGURE 7A.2 Indifference Curve and the Marginal Rate of Substitution The indifference curve shows the different combinations of movies and books that generate the same utility level. The slope is the marginal rate of substitution (MRS) between the two goods. The MRS is eight books per movie between points b and i, but only one book per movie between points m and n. The indifference curve passing through points b, i, m, and n separates the combinations of books and movies into three groups: 1 Superior combinations. 2 Inferior combinations. 3 Equivalent combinations.

7A.1 CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 7 7A.1 CONSUMER CONSTRAINTS AND PREFERENCES indifference curve map A set of indifference curves, each with a different utility level. FIGURE 7A.3 Indifference Curve Map An indifference curve map shows a set of indifference curves, with utility increasing as we move northeasterly to higher indifference curves (from I1 to I2 to I3).

7A.2 The Tangency Condition CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 7 7A.2 MAXIMIZING UTILITY The Tangency Condition FIGURE 7A.4 Maximizing Utility: MRS Equals the Price Ratio To maximize utility, the consumer finds the combination of books and movies where an indifference curve is tangent to the budget line. At the utility-maximizing combination (point e), the marginal rate of substitution (the consumer’s own trade-off, shown by the slope of the indifference curve) equals the price ratio (the market trade-off, shown by the slope of the budget line).

7A.2 The Utility-Maximizing Rule: MRS = Price Ratio CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 7 7A.2 MAXIMIZING UTILITY The Utility-Maximizing Rule: MRS = Price Ratio utility-maximizing rule Pick the combination that makes the marginal rate of substitution equal to the price ratio.

A P L I C A T I O N 1 A P P E N D I X TO C H A P T E R 7 WHAT’S YOUR MRS? APPLYING THE CONCEPTS #1: To determine whether a consumer is making the best choice, what single question can you ask? We can use the utility-maximizing rule to determine whether consumers are doing the best they can. Suppose a firm has a fixed budget of $200 to spend on punch and cookies for its holiday party. The price of punch is $2 per cup and the price of cookies is $1 per cookie; both goods will, of course, be provided free of charge to workers at the party. The firm’s objective is to maximize the utility of the typical employee, and your job is to determine whether the company spent this year’s party budget wisely. Assume that all employees have identical tastes for cookies and punch, so data from a single person will apply to every employee. You can ask the typical employee a single question. What’s your question? “How many cookies would you be willing to trade for one cup of punch? If the answer is “two cookies per cup of punch,” the MRS equals the price ratio, and the firm did the best it could. On the other hand, if the answer is “five cookies per cup of punch,” the MRS exceeds the price ratio, and the firm could have generated higher utility with its $200 by providing more punch and fewer cookies.

A P L I C A T I O N 2 A P P E N D I X TO C H A P T E R 7 ONLINE MUSIC AND PIRACY APPLYING THE CONCEPTS #2: Why do consumers dislike the bundling of goods? FIGURE 7A.5 Internet Music Piracy and iTunes When music is sold as 15-song bundles on CDs, the consumer has three budget points (a, c, and d) rather than an entire budget line. If songs are sold individually, the consumer has a full budget line and can legally reach his or her ideal combination of 6 songs and 48 arcade games (point b).

A P L I C A T I O N 3 A P P E N D I X TO C H A P T E R 7 THE BIG DIFFERENCE BETWEEN $0.20 AND FREE! APPLYING THE CONCEPTS #3: How do consumers respond to free goods? A few years ago Amazon.com introduced free shipping for U.S. orders over $25. A consumer who bought a single book for less than $25 would pay about $4 in shipping, but if adding a second book to the order brought the book total to at least $25, shipping was free. The free-shipping offer decreased the effective price of any book that pushed the book order over $25, and sales increased dramatically. In France, the company offered cheap—but not free—shipping for orders over $25. Crossing the $25 threshold cut the shipping charge to only 1 franc, about $0.20. In contrast with the U.S. experience, book sales increased by a relatively small amount. The Amazon experiences in the United States and France illustrates a puzzle in consumer behavior. Cutting the shipping charge from $4 to zero had a huge effect, but cutting the charge to $0.20 didn’t have much of an effect. Consumers are highly responsive to freebies, and many firms incorporate free goods and services into their marketing.

7A.3 The Negatively Sloped Demand Curve CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 7 7A.3 DRAWING THE INDIVIDUAL DEMAND CURVE The Negatively Sloped Demand Curve With so many curves floating around, it is worth reviewing their roles in consumer decision making: • The budget line shows the affordable combinations of two goods, representing the consumer’s constraints. • An indifference curve shows the different combinations of two goods that generate the same utility level, representing the consumer’s preferences. • The demand curve shows how much of a single product a consumer is willing to buy at a particular price. To get the demand curve, we use both the budget line and indifference curves.

7A.3 The Negatively Sloped Demand Curve CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 7 7A.3 DRAWING THE INDIVIDUAL DEMAND CURVE The Negatively Sloped Demand Curve FIGURE 7A.6 Drawing the Demand Curve A decrease in the price of movies tilts the budget line outward. In Panel A, the indifference curve is tangent to the new budget line at point t, with a larger quantity of movies (7 instead of 4). In Panel B, when the price of movies is $3, the consumer maximizes utility with 4 movies. A decrease in price to $2 increases the utility-maximizing number of movies to 7, illustrating the law of demand.

7A.3 The Income and Substitution Effects of a Price Change CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 7 7A.3 DRAWING THE INDIVIDUAL DEMAND CURVE The Income and Substitution Effects of a Price Change substitution effect The change in quantity consumed that is caused by a change in the relative price of the good, with real income held constant. income effect The change in quantity consumed that is caused by a change in real income, with relative prices held constant.

7A.3 The Income and Substitution Effects of a Price Change CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 7 7A.3 DRAWING THE INDIVIDUAL DEMAND CURVE The Income and Substitution Effects of a Price Change Let’s take a closer look at a consumer’s response to a change in price. We will break down Maxine’s response to a decrease in price into two effects: • Substitution effect. A decrease in the price of movies decreases the price of movies relative to the price of other goods, such as books. As movies become less costly relative to books, Maxine substitutes movies for books. • Income effect. A decrease in the price of movies increases Maxine’s real income (the purchasing power of her nominal income), and she will buy more of all normal goods. If watching movies is a normal good, she will watch more movies.

7A.3 The Income and Substitution Effects of a Price Change CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 7 7A.3 DRAWING THE INDIVIDUAL DEMAND CURVE The Income and Substitution Effects of a Price Change FIGURE 7A.7 The Substitution Effect of a Decrease in Price To observe the substitution effect, shown by the move from point e to point s, we offset the decrease in price of movies (from $3 to $2) by decreasing the consumer’s income to $26, thereby making the original choice (point e) just affordable. At the original choice, the MRS (three books per movie) exceeds the new price ratio (two books per movie), so the consumer can do better. Moving from point e to point s, utility increases and the quantity of movies increases from four to six.

7A.3 The Income and Substitution Effects of a Price Change CONSUMER CHOICE WITH INDIFFERENCE CURVES A P P E N D I X TO C H A P T E R 2 2 7A.3 DRAWING THE INDIVIDUAL DEMAND CURVE The Income and Substitution Effects of a Price Change FIGURE 7A.8 The Income Effect of a Decrease in Price To observe the income effect, shown by the move from point s to point t, we restore the consumer’s original nominal income of $30 (up from the $26 used to reveal the substitution effect) while keeping a price of $2 per movie. The budget line shifts outward, and the consumer maximizes utility at point t, so the quantity of movies increases from six to seven.

A P L I C A T I O N 4 THE SUBSTITUTION EFFECT OF A GAS TAX DECREASES GAS CONSUMPTION APPLYING THE CONCEPTS #4: How do consumers respond to offsetting changes in taxes? FIGURE 7A.9 Increasing the Gas Tax and Decreasing the Income Tax If a $2 gasoline tax is combined with a $2,000 decrease in the income tax, a person who initially buys 1,000 gallons (point a) can still afford the initial choice. But the increase in the relative price of gasoline means that the initial point no longer maximizes utility. At point a, the MRS is less than the new price ratio, and the substitution effect moves the consumer from point a to point b, reducing gasoline consumption from 1,000 to 700 gallons.

K E Y T E R M S budget line budget set income effect indifference curve indifference curve map marginal rate of substitution (MRS) price ratio substitution effect utility utility-maximizing rule